A narrow belt is used to drive a 20.00-cm diameter pulley from a 35.00-cm-diameter pulley. The centers of the two pulleys are 2.000 m apart. How long must the belt be if the pulleys rotate in the same direction? In opposite directions?
I am sure the solution to this problem is very simple, but I just cannot seem to figure out how to even begin this problem.Any help would be appreciated.
spideyunlimit
Sep3-08, 05:06 AM
I think you just need to find the hypotenuse using trigonometry.
Redbelly98
Sep3-08, 09:00 AM
... I just cannot seem to figure out how to even begin this problem.
Solving this begins with drawing a picture of the wheels and belt.
ur5pointos2sl
Sep3-08, 07:07 PM
Solving this begins with drawing a picture of the wheels and belt.
well of course that would be the obvious thing to do. Once i have it drawn I am guessing I need to form a right triangle? Simply by extending a tangent line from one pulley to the other on top and bottom? From here i am stuck. I know that the center is 2 cm but how do you calculate for the belt wrapping around the pulley itself? Would that be arc length or something?
tiny-tim
Sep3-08, 07:13 PM
Hi ur5pointos2sl! :smile:
… how do you calculate for the belt wrapping around the pulley itself? Would that be arc length or something?
Yes, that's arc-length! :smile:
Redbelly98
Sep4-08, 07:09 PM
well of course that would be the obvious thing to do.
Okay, guess I took you too literally when you said you didn't know how to begin.
Once i have it drawn I am guessing I need to form a right triangle? Simply by extending a tangent line from one pulley to the other on top and bottom? From here i am stuck. I know that the center is 2 cm but how do you calculate for the belt wrapping around the pulley itself? Would that be arc length or something?
Pretty much. Draw simple shapes like right triangles, rectangles, and/or circles to figure things out. Yes, the length of belt portion wrapping around the pulley is an arc length; you'll need to figure out the angle involved using geometry and trig.